Francisco A. Leon

Modeling gate leakage current in nMOS structures due to tunneling through an ultra-thin oxide

Abstract For the first time, the tunneling current in silicon nMOS structures with ultra-thin gate oxides has been studied both by numerically solving Schrodingers equation and by using the WKB approximation, which explicitly includes the size quantization effects in the inversion layers. The numerical solution employs first-order perturbation within the one-band effective-mass approximation to calculate the lifetime of an inversion-layer quasi-bound state. The good agreement in the tunneling currents estimated with these two methods justifies the use of the WKB approximation in the direct tunneling regime. The range of validity of the WKB approximation is also discussed.

Laser alignment modeling using rigorous numerical simulations

This paper describes a three-dimensional computer modeling technique for alignment system simulation, and some example calculations. The technique has been developed to address issues of alignment and overlay accuracy for future generation VLSI technology. The analytical basis is a general finite element electromagnetic wave propagation code, EMFlex, that rigorously simulates light scattering from the 3-D alignment mark. Using the Nikon Laser Step Alignment (LSA) system as a model instrument, the overlay error and signal shape are simulated. Examples of an idealized asymmetric metal mark are studied. Preliminary results suggest that the rigorous simulations are substantially different from the one-dimensional Fresnel approximations that have been used previously.

Numerical modeling of glass flow and spin-on planarization

A model for the flow of phosphosilicate glass (PSG) and borophosphosilicate glass (BPSG) has been developed and integrated into the SAMPLE process simulation program. The physical basis of the model is the deformation of the glass in such a way as to decrease the surface free energy; the kinetics of the deformation are assumed to be controlled by a surface diffusion process. The model is applicable to 2-D and quasi-3-D (cylindrically symmetric) structures. In addition, a related model has been developed for spin-on glass, polyimide, and photoresist. The theory of these models is discussed, and examples of simulations using these models are presented. >

Stability Issues in Self-Consistent Monte Carlo-Poisson Simulations

This paper investigates the time stability of self-consistent Monte Carlo-Non Linear Poisson simulations (MC-NLP). A simplified analytical stability theory has been developed and verified by means of extensive simulations. The properties of the MC-NLP scheme are compared to those of Monte Carlo-Linear Poisson (MC-LP) scheme. The influence of statistics collection and charge assignment algorithms is also analyzed.

Fast algorithms for 3D high NA lithography simulation

Partial coherent imaging in a high NA stepper is treated with the source integration method. Image formation in 3D is accomplished by the propagation and interference of plane waves. This approach allows the extensive use of FFT and leads to efficient computation of the latent image. In order to further reduce the computation time, we propose a sufficient condition for the grid density in an image plane based on the sampling theorem. Finally, we present a semi-analytical method for the modeling of post exposure bake process in 3D. With these enhancements in the algorithm, a typical 3D latent image problem can be solved in a few second on a workstation.

Predicting mask performance by numerical simulation

In this paper, we present a method for linking a finite element Maxwells equation solver with a scalar lithography simulator, iPHOTO-II. The combined simulator takes the mask topography and the stepper parameters as input and simulates the resist profile on the wafer plane. The accuracy of the simulator is demonstrated by comparing simulation results with experimental data over a wide range of focus, exposure and mask dimensions. The simulator is used to predict the performance of a phase edge phase shift mask. It is revealed that the true position of the line center in a phase edge PSM is shifted slightly from the location given by geometric projection. Biasing rules for compensating for this location shift are presented.

An Efficient Sample/Monte Carlo Methodology For Developing Robust Photolithography Processes

The development of robust photolithography processes requires methodologies for efficiently finding operating conditions that will minimize the sensitivity of critical dimension control to the effects of inevitable manufacturing variability. Photolithography modeling coupled with a Monte Carlo sampling scheme and contemporary statistical design techniques accelerate the identification of the best operating conditions by reducing the number of needed process development experiments.